Question: Simplify the following expression: $\dfrac{4z^2}{36z^3}$ You can assume $z \neq 0$.
Explanation: $ \dfrac{4z^2}{36z^3} = \dfrac{4}{36} \cdot \dfrac{z^2}{z^3} $ To simplify $\frac{4}{36}$ , find the greatest common factor (GCD) of $4$ and $36$ $4 = 2 \cdot 2$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(4, 36) = 2 \cdot 2 = 4 $ $ \dfrac{4}{36} \cdot \dfrac{z^2}{z^3} = \dfrac{4 \cdot 1}{4 \cdot 9} \cdot \dfrac{z^2}{z^3} $ $\phantom{ \dfrac{4}{36} \cdot \dfrac{2}{3}} = \dfrac{1}{9} \cdot \dfrac{z^2}{z^3} $ $ \dfrac{z^2}{z^3} = \dfrac{z \cdot z}{z \cdot z \cdot z} = \dfrac{1}{z} $ $ \dfrac{1}{9} \cdot \dfrac{1}{z} = \dfrac{1}{9z} $